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Manuscript Title: New efficient programs to calculate general recoupling coefficients. Part II: evaluation of a summation formula.
Authors: V. Fack, S.N. Pitre, J. Van der Jeugt
Program title: NJSUMMATION, NJSUMPAR
Catalogue identifier: ADBA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 86(1995)105
Programming language: C.
Computer: 386/486-BASED PCs.
Operating system: MS-DOS, LINUX, UNIX.
Keywords: Atomic structure, Nuclear structure, General purpose, Scattering, General recoupling Coefficient, Angular momentum, Racah coefficient, 3n-j coefficient, Recursive techniques, Arbitrary nested loops, Parallel processing, Transputer, Farming technique, Rotation group.
Classification: 4.1.

Subprograms used:
Cat Id Title Reference
ACVV_v1_0 NJFORMULA CPC 83(1994)275

Nature of problem:
A general recoupling coefficient for an arbitrary number of (integer or half-integer) angular momenta can be expressed as a formula consisting of products of 6-j coefficients summed over a certain number of variables. Such a formula can be generated using the program NJFORMULA [1]. The present programs perform the evaluation of a generated formula for given data of angular momenta.

Solution method:
A summation formula for a general recoupling coefficient can contain an arbitrary number of summation variables, which is determined by the binary trees involved in the search process when generating the formula [1]. To develop a general algorithm for the evaluation of such a formula, we use recursive programming techniques which allow to implement arbitrary nested loops. Apart from the sequential implementation NJSUMMATION of this algorithm, we also present a parallel version NJSUMPAR, which can be executed on a network of transputers. The latter uses a farming technique, where a master processor distributes work packets to several worker processors who calculate products of 6-j coefficients.

Running time:
For the sequential program the running time is determined mainly by the number of 6-j coefficients computed in the evaluation process. Typical examples, involving up to ten thousand 6-j coefficients, take less than 0.25 seconds on the Sun Sparc, less than 0.5 seconds on the 486-based PC, and less than 50 seconds on a single T800 transputer. More complicated examples, involving up to one million 6-j coefficients, take less than 20 seconds on the Sun Sparc and less than 40 seconds on the 486-based PC. For the parallel program we focus our attention on the advantage factor of the parallel version compared with the sequential version. On a network of 4 transputers, the parallel program is 3 to 4 times faster than the corresponding sequential version.

References:
[1] V. Fack, S.N. Pitre, J. Van der Jeugt, Comp. Phys. Commun. 83(1994)275.